DETERMINATION OF THE MOLECULAR WEIGHT
AND
pKa OF AN UNKKNOWN ACID
INTRODUCTION:
In this experiment, you will determine the equivalent mass of an unknown acid, that is, the mass
of the acid that supplies one mole of hydrogen ions. The acid, a solid crystalline substance, will
be weighed out and titrated with a standard solution of sodium hydroxide. From the moles of
base used and the mass of the acid, you will be able to determine the equivalent mass of the acid.
Next you will plot the titration curve of the acid, with pH on the vertical axis and the volume of
NaOH on the horizontal axis. From this graph you will be able to determine the value of the
equilibrium constant for the dissociation of the acid.
Acids are substances that contain ionizable hydrogen atoms within the molecule. Strong acids
ionize totally, weak acids partially. The value of Ka, the equilibrium constant for the dissociation
of the acid, is an indication of the strength of the acid. We can also speak of the pKa, the
–log(Ka), as an indication of the acid strength.
The concentration of the NaOH solution must be accurately known. To “standardize” the NaOH,
that is to find its exact molarity, the NaOH is titrated against a solid acid, potassium hydrogen
phthalate, sometimes abbreviated KHP. The KHP is chosen because it is easily dried and
weighed, and has a relatively high equivalent mass. The formula of KHP is:
O
C
C
OH
OK
or KHC8H4O4
It contains one ionizable
H+1. The titration can
be followed using
phenolphthalein as an
indicator.
O
A graph of pH versus mL of NaOH added can be drawn by carefully following the titration with a
pH meter. There should be a significant change in pH in the vicinity of the equivalence point.
Note that the equivalence point will probably NOT be pH 7, but will be on the basic side. The
value of the equilibrium constant for the dissociation of the acid can be obtained from the graph.
If we represent the dissociation of the acid as:
HA + H2O
H3O+1 + A-1
The equilibrium expression is:
Ka 
[H 3 O 1 ][A -1 ]
[HA]
When the acid is half neutralized, [HA] = [A-1], so these terms cancel in the above equation, and
Ka = [H3O+1] therefore, when the acid is half-neutralized, the pH = pKa. The point where pH is
equal to pKa can be found from the graph. Refer to Figure 1.
43
DETERMINATION OF THE MOLECULAR WEIGHT
AND
pKa OF AN UNKKNOWN ACID
pH Change During Titration
pH
C
B
A
Volume of NaOH
Figure 1. pH during Titration of a Monoprotic Weak Acid with Sodium Hydroxide
Where
A = Volume NaOH at equivalence point
B = ½ volume of A or the volume when half-neutralized
C = pH when half neutralized, or pKa
If the acid contains two ionizable hydrogen atoms, the titration curve shows two separate
inflections corresponding to the neutralization of each separate hydrogen. Figure 2 shows a
titration curve for a diprotic acid such as H2A. The dissociation of a diprotic acid can be written
in two separate steps:
H2A + H2O
H3O+1 + HA-1
HA-1 + H2O
H3O+1 + A-2
The two equilibrium expressions are:
K a1 
[H 3 O 1 ][HA -1 ]
[H 2 A]
K a2 
[H 3 O 1 ][A -2 ]
HA -1 ]
If a diprotic acid is titrated, two inflections will be present if the pKa values differ by 4 or more
pK units. If this is the case, both pKa values can be determined from the graph of pH versus
volume of sodium hydroxide added. Refer to Figure 2 to see how this is done.
44
DETERMINATION OF THE MOLECULAR WEIGHT
AND
pKa OF AN UNKKNOWN ACID
pH Change During Titration
of Diprotic Acid
F
pH
E
D
B
C
A
Volume of NaOH
Figure 2. pH During Titration of a Diprotic Acid with Sodium Hydroxide
Where
B represents the volume of sodium hydroxide needed to react with one of the acid hydrogens
A represents the volume of sodium hydroxide needed to react with both of the acid hydrogens
D is the volume of sodium hydroxide needed to neutralize half of the first acid hydrogen
E represents the pH when half of the first hydrogen is neutralized, or pKa1
C represents the volume of sodium hydroxide used when all of the first hydrogen and half of
the second are neutralized
F is the pH when half of the second hydrogen is neutralized, or pKa2.
At the first equivalence point, all H+ ions from the first dissociation have reacted with
NaOH base. At the second equivalence point, all H+ ions from both reactions have
reacted (twice as many as at the first equivalence point). Therefore, the volume of NaOH
added at the second equivalence point is exactly twice that of the first equivalence point.
The primary purpose of this experiment is to identify an unknown diprotic acid by
finding its molecular weight. A diprotic acid is titrated with NaOH solution of known
concentration. Molecular weight (or molar mass) is found in g/mole of the diprotic acid.
Weighing the original sample of acid will tell you its mass in grams. Moles can be
determined from the volume of NaOH titrant needed to reach the first equivalence point.
The volume and the concentration of NaOH titrant are used to calculate moles of NaOH.
Moles of unknown acid equal moles of NaOH at the first equivalence point. Once grams
and moles of the diprotic acid are known, molecular weight can be calculated, in g/mole.
Molecular weight determination is a common way of identifying an unknown substance
in chemistry.
You may use either the first or second equivalence point to calculate molecular weight.
The first is somewhat easier, because moles of NaOH are equal to moles of H2X. If the
second equivalence point is more clearly defined on the titration curve, however, simply
divide its NaOH volume by 2 to confirm the first equivalence point; or use the ratio:
1 mole H2X / 2 mol NaOH
45
DETERMINATION OF THE MOLECULAR WEIGHT
AND
pKa OF AN UNKKNOWN ACID
CHEMICALS:
Sodium Hydroxide, 6 M
Weak acid, solid
Baking soda, NaHCO3
Phenolphthalein
Potassium hydgrogen phthalate, KHC8H4O4(s)
Vinegar, HC2H3O2
EQUIPMENT:
Windows PC
Vernier computer interface
Logger Pro
Vernier pH Sensor
Bottle, 1-L
Erlenmeyer flask, 250 mL
50-mL Buret
Wash Bottle
Beaker, 250-mL
Weighing boats (2)
Balance, sensitive
Weighing boat
Ring stand and buret clamp
Utility clamp
Desiccator
PROCEDURE:
1. Preparation and Standardization of Approximately 0.12 M NaOH
Since solid NaOH rapidly absorbs both H2O and CO2, a solution of exact molarity cannot be
prepared by weighing the solid and diluting to volume. Instead, you must prepare a solution of
approximately the desired concentration, and find its exact molarity by titrating it against a
standard substance.
Clean a 1 liter bottle and rinse with distilled water.
Measure approximately 18 mL of 6 M NaOH, and dilute to about 1 liter with distilled water. Use
freshly distilled water so that the recent boiling has removed any dissolved CO2 that would react
with the NaOH.
Mix very well
Obtain a sample of potassium hydrogen phthalate (KHP) which has been dried in an oven and
stored in a desiccator, and use a sensitive balance to accurately weigh 0.4 to 0.6 grams into a
weighing boat. Wash the KHP into an Erlenmeyer flask using distilled water from a wash bottle.
Add about 40 mL of distilled water and swirl until completely dissolved.
Clean a buret, rinse it with distilled water and then three times with small (about 7 mL) portions
of your NaOH solution (don’t forget to rinse the tip), and then fill it with your NaOH solution.
Open the stopcock briefly and shake the buret vertically to remove air bubbles from the tip.
Add 3 drops of phenolphthalein solution to the acid in the flask and then titrated with the NaOH
until the first trace of pink color persists for 15 seconds. Remember to constantly swirl the flask,
and to rinse the walls of the flask with distilled water before you reach the end point. Record the
volume of NaOH used, estimating the nearest 0.01 mL.
46
DETERMINATION OF THE EQUIVALENT MASS
AND
pKa OF AN UNKKNOWN ACID
Repeat two more times. If you use slightly more acid each time, the second and third titrations
will be much more rapid than the first because you will know how much NaOH you can safely
add before you get close to the end point.
Calculate the average molarity of your NaOH solution.
2. Determination of the Molecular Weight of an Unknown Acid.
Accurately weigh a sample of your unknown acid into a weighing boat using the sensitive
balance. You should weigh about 0.3-0.4 grams of sample.
Use a utility clamp to suspend a pH Sensor on a ring stand as shown in Figure 2. Position
the pH Sensor in the diprotic acid solution and adjust its position toward the outside of
the beaker so that it is not struck by the stirring bar.
Obtain a 50-mL buret and rinse the buret with a few mL of the ~6 M NaOH solution.
Record the precise concentration of the NaOH solution in the Data and Calculations
table. Use a utility clamp to attach the buret to the ring stand as shown in Figure 2. Fill
the buret a little above the 0.00-mL level of the buret. Drain a small amount of NaOH
solution so it fills the buret tip and leaves the NaOH at the 0.00-mL level of the buret.
Dispose of the waste solution from this step as directed by your teacher. CAUTION:
Sodium hydroxide solution is caustic. Avoid spilling it on your skin or clothing.
Prepare the computer for data collection by opening the file in the Experiment 25 folder
of Chemistry with Computers. The vertical axis of the graph has pH scaled from 0 to 14
pH units. The horizontal axis has volume scaled from 0 to 25 mL. The live Meter window
below the graph should show a pH value between 0.0 and 0.5.
You are now ready to begin the titration. This process goes faster if one person
manipulates and reads the buret while another person operates the computer and enters
buret readings.
a. Before adding NaOH titrant, click Collect and monitor pH for 5-10 seconds. Once
the pH has stabilized, click Keep . In the edit box, type “0” (for 0 drops added),
and press ENTER to store the first data pair for this experiment.
b. Add enough NaOH to raise the pH by about 0.20 units. When the pH stabilizes,
again click Keep . In the edit box, type the current buret reading, to the nearest
0.01 mL. Press ENTER. You have now saved the second data pair for the
experiment.
c. Continue adding NaOH solution in increments that raise the pH about 0.20 units
and enter the buret reading after each addition. Proceed in this manner until the
pH is 3.5.
d. When pH 3.5 is reached, change to 2-drop increments. Enter the buret reading
after each increment.
e. After pH 4.5 is reached, again add larger increments that raise the pH by about
0.20 units and enter the buret reading after each addition. Continue in this manner
until a pH of 7.5 is reached.
f. When pH 7.5 is reached, change to 2-drop increments. Enter the buret reading
after each increment.
g. When pH 10 is reached, again add larger increments that raise the pH by 0.20
units. Enter the buret reading after each increment. Continue in this manner until
you reach a pH of 11.
47
DETERMINATION OF THE EQUIVALENT MASS
AND
pKa OF AN UNKKNOWN ACID
When you have finished collecting data, click
down the drain.
Stop
. Dispose of the beaker contents
Print a copy of the Table window. Enter your name(s) and the number of copies of the
table.
Print a copy of the Graph window. Enter your name(s) and the number of copies of the
graph.
Repeat one more time. Choose a mass for the second sample so that the volume of NaOH needed
will be about 40 mL.
3. Determination of the pKa of the Unknown Acid.
Determine the precise NaOH volume for the first half-titration point using one-half of the
first equivalence point volume (determined in Step 2 or Step 9 of Processing the Data).
Then determine the precise NaOH volume of the second half-titration point halfway
between the first and second equivalence points.
On your graph of the titration curve, draw reference lines similar to those shown in
Figure 2. Start with the first half-titration point volume (point D) and the second halftitration point volume (Point C). Determine the pH values on the vertical axis that
correspond to each of these volumes. Estimate these two pH values to the nearest 0.1 pH
unit. These values are the pKa1 and pKa2 values, respectively. (Note: See if there are
volume values in your data table similar to either of the half-titration volumes in Step 1.
If so, use their pH values to confirm your estimates of pKa1 and pKa2 from the graph.)
From the pKa1 and pKa2 values you obtained in the previous step, calculate the Ka1 and Ka2
values for the two dissociations of the diprotic.
PROCESSING THE DATA:
1. On your printed graph, one of the two equivalence points is usually more clearly
defined than the other; the two-drop increments near the equivalence points
frequently result in larger increases in pH (a steeper slope) at one equivalence point
than the other. Indicate the more clearly defined equivalence point (first or second) in
the Data and Calculations table.
2. Use your graph and data table to determine the volume of NaOH titrant used for the
equivalence point you selected in Step 1. To do so, examine the data to find the
largest increase in pH values during the 2-drop additions of NaOH. Find the NaOH
volume just before this jump. Then find the NaOH volume after the largest pH jump.
Underline both of these data pairs on the printed data table and record them in the
Data and Calculations table.
48
DETERMINATION OF THE EQUIVALENT MASS
AND
pKa OF AN UNKKNOWN ACID
3. Determine the volume of NaOH added at the equivalence point you selected in Step
1. To do this, add the two NaOH volumes determined in Step 2, and divide by two.
For example:
12.34 + 12.44
= 12.39 mL
2
4. Calculate the number of moles of NaOH used at the equivalence point you selected in
Step 1.
5. Determine the number of moles of the diprotic acid, H2X. Use Equation 3 or Equation
5 to obtain the ratio of moles of H2X to moles of NaOH, depending on which
equivalence point you selected in Step 1.
6. Using the mass of diprotic acid you measured out in Step 1 of the procedure, calculate
the molecular weight of the diprotic acid, in g/mol.
7. From the following list of five diprotic acids, identify your unknown diprotic acid.
Diprotic Acid
Oxalic Acid
Malonic Acid
Maleic Acid
Malic Acid
Tartaric Acid
Formula
H2C2O4
H2C3H2O4
H2C4H2O4
H2C4H4O5
H2C4H4O6
Molecular weight
90
104
116
134
150
8. Determine the percent error for your molecular weight value in Step 6.
9. For the alternate equivalence point (the one you did not use in Step 1), use your
graph and data table to determine the volume of NaOH titrant used. Examine the data
to find the largest increase in pH values during the 2-drop additions of NaOH. Find
the NaOH volume just before and after this jump. Underline both of these data pairs
on the printed data table and record them in the Data and Calculations table. Note:
Dividing or multiplying the other equivalence point volume by two may help you
confirm that you have selected the correct two data pairs in this step.
10. Determine the volume of NaOH added at the alternate equivalence point, using the
same method you used in Step 3.
11. On your printed graph, clearly specify the position of the equivalence point volumes
you determined in Steps 3 and 10, using dotted reference lines like those in Figure 1.
Specify the NaOH volume of each equivalence point on the horizontal axis of the
graph.
49
DETERMINATION OF THE EQUIVALENT MASS
AND
pKa OF AN UNKKNOWN ACID
DATA TABLE:
Mass of diprotic acid
g
Concentration of NaOH
M
1. Equivalence point (indicate which one you will use
in the calculations below)
2. NaOH volume added before and after the largest
pH increase
first equivalence point
or
second equivalence point
______ mL
——
——
______mL
3. Volume of NaOH added at the equivalence point
mL
4. Moles of NaOH
mol
5. Moles of diprotic acid, H2X
mol
6. Molecular weight of diprotic acid
g/mol
7. Name, formula, and accepted molecular weight of
the diprotic acid
___________ ___________ _______
g/mol
8. Percent error
%
9. Alternate equivalence point (indicate the one used
in the calculations below)
10. NaOH volume added before and after the largest
pH increase
first equivalence point
or
second equivalence point
______ mL
——
——
______mL
11. Volume of NaOH added at the alternate
equivalence point
mL
50
DETERMINATION OF THE EQUIVALENT MASS
AND
pKa OF AN UNKKNOWN ACID
Preliminary Lab Assignmnet
1. What is the molecular weight of each of the following acids?
a. HC2H3O2
b. KHCO3
c. H2SO3
2. Calculate the molarity of a solution of sodium hydroxide if 23.64 mL is needed to neutralize
0.5632 grams of potassium hydrogen phthalate.
3. It is found that 24.68 mL of 0.1165 M NaOH is needed to titrated 0.2931 grams of an
unknown acid to the phenolphthalein end point. Calculate the molecular mass of the acid.
4. The following values were experimentally determined for the titration of 0.145 grams of a
weak acid with 0.100 M NaOH:
Volume of NaOH, mL
0.00
5.00
10.00
12.50
15.00
20.00
24.00
24.90
25.00
26.00
30.00
pH
2.88
4.15
4.58
4.76
4.93
5.36
6.14
7.15
8.73
11.29
11.96
51
DETERMINATION OF THE EQUIVALENT MASS
AND
pKa OF AN UNKKNOWN ACID
a. Graph the data on the chart below:
Change of pH during Titration of Weak Acid with NaOH
14
13
12
11
10
9
8
pH 7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
Volume of 0.100 M NaOH in mL
b. What is the pH at the equivalence point?
c. Does the acid appear to be monoprotic or diprotic? Explain.
d. Give the Ka and pKa value (or values) of the acid.
e. Calculate the molecular weight of the acid.
52